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Uniform approximation by universal series on arbitrary sets

Published online by Cambridge University Press:  01 January 2008

VANGELIS STEFANOPOULOS
VANGELIS STEFANOPOULOS*
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, 1678 Nicosia, Cyprus. e-mail: vstefan@ucy.ac.cy
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Abstract

By considering a tree-like decomposition of an arbitrary set we prove the existence of an associated series with the property that its partial sums approximate uniformly all elements in a relevant space of bounded functions. In a topological setting we show that these sums are dense in the space of continuous functions, hence in turn any Borel measurable function is the almost everywhere limit of an appropriate sequence of partial sums of the same series. The coefficients of the series may be chosen in c0, or in a weighted ℓp with 1 < p < ∞, but not in the corresponding weighted ℓ1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 1 , January 2008 , pp. 207 - 216
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

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